One interesting thought, on the W10 machine I'm writing this (v1511:b10586.29), W10 is not activated, and you cannot change Themes, or backgrounds (wallpapers), or much of anything else unless your W10 is activated. Did you perform an upgrade from an earlier version of Windows (such as Win7 or Win8/8.1)? Was that Windows version licensed? Or did your PC come with W10 pre-installed? If so, your upgrade to W10 should now be also Activated. If you type in "THIS PC" next to the W10 Start Flag in the lower left of your W10 desktop, and click on "Properties", look under "Windows Activation". If not activated, you won't be able to make any changes to your desktop.
However, if your Windows Activation shows "Activated", then you have the...